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Question

A resistance of 4 Ω and a wire of length 5 m and resistance 5 Ω are joined in series and connected to a cell of e.m,f, 10V and internal resistance 1 Ω. A Parallel combination of two identical cells is balanced across 300 cm of the wire. the e.m.f. E each cell is then:
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A
1.5 V
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B
3.0 V
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C
0.67V
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D
1.33 V
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Solution

The correct option is B 3.0 V
In the potentiometer circuit, net resistance,
R1=5+4+1=10Ω (due to wire +4Ωseries resistor & internal resistance of cell ).
and any provide E1=10V.
For secondary circuit,
equivalent any of cells is parallel, E=E ( as no internal resistance)
and resistance =55×3=3Ω (due to 3m balance length )
At balance length, both circuits have equal currents (I)
I=E1R1=E2R21010=E3E=3V.

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